How to win the jackpot - four times

A reclusive maths professor has won lottery scratchcard jackpots four times.
Luck? A secret strategy? An expert explains how she might have done it.

Her number's up: Joan Ginther has won almost £13 million buying lottery scratchcards from the same store in her Texan hometown

By Prof David Spiegelhalter

7:30AM BST 13 Aug 2011

It’s something we could never imagine in our wildest dreams. “Woman hits the lottery jackpot an astonishing FOUR times” proclaimed the headlines this week. Yes, that’s right – four times. An American woman, described as “the luckiest woman in the world” for rather obvious reasons, has won almost £13 million in recent years, becoming a global sensation.

So how has she done it? Is it plain luck – or can there possibly be a strategy for winning a fortune?

Joan Ginther won all her jackpots in the Texas Lottery’s high stakes scratchcard games. The 63-year-old’s winning streak started with a £3.3 million win in 1993. She won again in 2006 and 2008, and in 2010 she paid $50 (£31) for a scratchcard which won her a jackpot $10 million (£6.2 million). Her odds of winning all these prizes at first sight appear to be astronomical, akin to winning our version of the National Lottery a few times in a row. Lucky woman, you’re thinking.

We all want to believe in luck, and I don’t want to disabuse you: these wins certainly could be coincidence. My usual response to stories such as this is to point out that vast numbers of people buy these cards and these kinds of rare events do happen.

But as soon as I began to investigate Ginther’s story, a succession of other tell-tale “coincidences” began to emerge that made me think maybe this was not just chance at work.

Why did I think this? Well, first, Ginther won her haul on scratchcards. The lottery we watch on television, with balls drawn out of a drum, is entirely random, whereas the science of scratchcards is rather different.

Then there is the fact that Ginther is a maths professor. And last, she bought most of her scratchcards from the same petrol station in the small town of Bishop, Texas, where she grew up. It is reported she had a deal with the store owner, who would keep aside new batches of high-stake scratchcards for her to take away and inspect at her leisure.

Call me suspicious, but I began to doubt the role of luck in Joan Ginther’s wins.

Let me try to answer the million-dollar question of how she did it. We should start by looking at the nature of lotteries. It’s a completely random lucky draw, right?

This certainly is the case with the lottery numbers drawn out of a drum, and with the roulette wheel beloved of Hollywood films. Amateur gamblers like to believe there is a pattern that gives them a better-than-average chance of winning – that red on the roulette wheel is “due to win”, that you can only land on so many blacks before a change occurs, for instance.

This is known as the gamblers’ fallacy. There is, in fact, no pattern to these games. There is no way you can fiddle the odds, as generations of casino losers will attest. So, for example, knowing the history of numbers in our main TV lottery gives you no advantage at all. These gambles are completely unpredictable.

But there are other forms of gambling where you can tip the odds in your favour – through skill, knowledge or illegal activity. Some of these are well-known. In horse racing, you might use your judgment to select the better horse, increasing your odds of winning over the average punter. And if you have inside knowledge of a corrupt football referee’s plans, for example, you can place a winning bet that could put you on the wrong side of the law.

Then there are scratchcards. They are not random – somebody decides how many will deliver a win, and how the winning cards are spread geographically. The winning numbers are generated by a computer program according to a formula.

Cards that appear “almost” to win – for example, having three out of four of the matching symbols needed – are produced to encourage people to buy another card. There is no randomness involved, then – just uncertainty about what the formula is and how the cards are distributed. The technical term for this is epistemic uncertainty. The quantity of winning tickets is fixed – you just don’t know what, or indeed where, they are. But you can use information available to increase the odds of winning, or to figure out the algorithm or formula used to assign winning tickets. Think of it as code-breaking.

This possibility means that scratchcards are open to manipulation. It has been alleged that this has happened in the US and Canada, and may even have been used as a means of money-laundering.

There are several ways in which it could be done. You could analyse the spread and timing of winners and predict where a win is likely to occur.

You could also use the information given to you on the scratchcard. It is my understanding that Ginther won on cards known as “baited hooks”. They display a lot of numbers on the front of the cards and ask the gambler to match them in some way with the numbers that lie beneath the scratch-off latex. With careful mathematical analysis, the displayed numbers can give some information about whether the card is a winner.

In Britain the National Lottery Bingo cards are of this type – they cost £3 and have prizes of up to £300,000 (today Camelot is launching a £5 scratchcard with a top prize of £2 million). Naturally, lottery companies are reluctant to acknowledge that their games can be cracked. I am sure they also look for patterns of wins and guard against code-breakers.

Mohan Srivastava, a geological statistician living in Toronto, has spoken about how he began to analyse these “baited hook” scratchcards.

“The tickets are clearly mass-produced, which means there must be some computer program that lays down the numbers,” he says. “Of course, it would be really nice if the computer could just spit out random digits. But that’s not possible, since the lottery corporation needs to control the number of winning tickets [otherwise it could go bust]. The game can’t be truly random. Instead, it has to generate the illusion of randomness while actually being carefully determined.”

Srivastava realised that he could apply the logic he uses in geology to find “gold deposits” to crack the scratchcards. He analysed how many times a number appeared on each card. He worked out that if three unique numbers – that is, numbers that appeared only once on the card – were set in a row together, the card was probably a winner. He was able to predict 19 out of 20 of the games.

He also worked out he would make less trawling shops for winning cards than he does in his work as a consultant, and reported his find to the Ontario Lottery and Gaming Corporation, who withdrew the game.

Could you crack British scratchcards in the same way? If you are skilled at maths and do the work, you may be able to improve your odds a little. Like Ginther, you would need to find an amenable shop assistant who would let you look through the cards, and you would have to make a substantial investment in time and money in order to find a winning card.

My guess is that Professor Ginther spent a lot on cards over the years (they cost between £12-£31), and she would have won a vast number of smaller prizes – but was also lucky enough to get some jackpots too.

Like Srivastava, I would prefer to stick with my day job. But I do like to think that Joan Ginther’s story could inspire our next generation of students to concentrate very hard indeed on their maths.

David Spiegelhalter is the Winton Professor of the Public Understanding of Risk at Cambridge University’s Statistical Laboratory. He was speaking to Zoe Brennan.